According to a team of medical professionals (via a 2007 study article published in the BMJ), the short answer is that no, human hair does not continue to grow after one’s death.
The growth of one’s hair and nails requires a hormonal regulation sequence that does not, and cannot, occur after death. Underneath hair follicles lies a cluster of cells called the hair matrix. These cells receive energy from the burning of glucose, and then use that energy to stimulate the hair follicles and eventually create hair growth. Glucose burning, however, is contingent upon the body’s receipt of oxygen, which, of course, cannot occur while deceased (via StatPearls).
Human fingernails are quite similar, in this context. Cell production underneath the nail beds promotes fingernail growth, and the process of this cell production is contingent upon glucose. Without glucose, which, again, cannot be supplied during death, the fingernails cannot grow.